A microlithographic projection exposure apparatus serves for the generation of structures on a substrate in the form of a semiconductor wafer during the production of semiconductor components. To this end, the projection exposure apparatus includes a projection lens having a plurality of optical elements, for imaging mask structures on the wafer during the exposure process.
A projection lens with wavefront aberrations that are as small as possible is desirable to image the mask structures on the wafer as precisely as possible. Therefore, projection lenses are equipped with manipulators, which render it possible to correct wavefront errors by changing the state of individual optical elements of the projection lens. Examples for such a state change include: a change in position in one or more of the six rigid body degrees of freedom of the relevant optical element, an impingement of the optical element with heat and/or coldness, a deformation of the optical element or a material ablation at the optical element via a post-processing device. Within the scope of this application, such a post-processing device is also understood as a manipulator of the projection lens in the general sense thereof.
Changes of the manipulator to be carried out in order to correct an aberration characteristic of a projection lens are calculated via a travel-generating optimization algorithm, which is also referred to as “manipulator change model”. By way of example, such optimization algorithms are described in WO 2010/034674 A1.
Thus, optimization algorithms known from the prior art may be configured to solve the following optimization problem:min∥Mx−bmess∥22 with NB:Fi(x)≦specxi 
Such an optimization problem is configured to minimize the merit function, also referred to as figure-of-merit function, described by ∥Mx−bmess∥22, taking into account constraints described by Fi (x)≦specxi. Here, M denotes a sensitivity matrix, x denotes a travel vector with travels for the individual manipulators, bmess denotes a state vector of the projection lens which describes a measured aberration characteristic of the projection lens, ∥ ∥2 denotes the Euclidean norm and specxi denotes a respective fixed limit for individual travels xi.
Here, a “travel” is understood to mean a change in the state variable of an optical element, carried out via manipulator actuation, along the travel for the purposes of changing the optical effect thereof. Such a travel defined by changes in the state variable of the optical element is specified by way of target change variables of the associated manipulator. By way of example, the manipulation can consist of the displacement of the optical element in a specific direction, but it can also consist of e.g. an impingement, in particular a local or two-dimensional impingement, of the optical element with heat, coldness, forces, light with a specific wavelength or currents. Furthermore, the manipulation can define material ablation at an optical element, which is to be carried out via a post-processing device. By way of example, the target change variable can define a path length to be covered or an angular range to be covered in the case of a displacement.
The constraints defined by Fi(x)≦specxi provide hard displacement limits for the manipulators, which may not be exceeded. The optimization result in the form of a travel command generated thereby is not ideal for all manipulator configurations.